With reference to FIG. 22, explanation is made on the mechanical resonator in the prior art. FIG. 22 is a view showing, with simplification, a structure of a mechanical vibration filter introduced in the document, Frank D. Bannon III, John R. Clark, and Clark T.-C. Nguyenc, “High-Q HF Microelectromechanical Filters” (IEEE Journal of Solid-State Circuits, Vol. 35, No. 4, pp. 512-526, April 2000).
This filter is formed with a thin film formed over a silicon substrate. The structure is with an input line 104, an output line 105, both-end-supported beams 101, 102 arranged with a spacing of 1 micron or less to the lines, and a joint beam 103 joining the two beams together. The signal inputted at the input line 104 is capacitively coupled with the beam 101, to cause an electrostatic force on the beam 101. Mechanical vibration is caused only when the signal frequency agrees with or is very close to the resonant frequency of the elastic structure formed by the beams 101, 102 and the joint beam 103. By detecting the mechanical vibration as a change of capacitance between the output line 105 and the beam 102, a filtered output of the input signal can be withdrawn.
When taking elasticity E, density ρ, thickness h and length L for a both-end-supported beam having a rectangular section, the resonant frequency f is given by the following equation.
                    f        =                  1.03          ⁢                                          ⁢                      h                          L              2                                ⁢                                    E              ρ                                                          (        1        )            Provided that the material is polysilicon, E=160 GPa and ρ=2.2×103 kg/cm3 result. Meanwhile, provided that the dimensions are L=40 μm and h=1.5 μm, f=8.2 MHz results. Thus, a filter at approximately 8 MHz can be structured. The use of mechanical resonance makes it possible to obtain a sharp frequency selective characteristic having a high Q value as compared to the filter constituted by a passive circuit, such as a capacitor and a coil.
However, the conventional structure encounters a restriction in constituting a higher-frequency band filter. Namely, it is clear from (equation 1) that, firstly, E/ρ is to be increased by changing the material. However, when E is taken greater, the displace amount of the beam decreases even at the equal force deforming the beam, which makes it difficult to detect a displacement of the beam. Meanwhile, in case the index representative of a beam bendability is taken d/L that is a ratio of a deformation amount d at the center of the both-end-supported beam and a beam length L where a static load is applied to a surface of the beam, d/L is expressed by the following proportional relationship.
                              d          L                ∝                                            L              3                                      h              3                                ·                      1            E                                              (        2        )            
From those, in order to raise the resonant frequency while keeping the value of d/L, a material with a low density p must be sought because at least E cannot be changed. There is a need to use a composite material, such as CFRP (carbon fiber reinforced plastics), as a material equivalent in Young's modulus to polysilicon and low in density. In this case, there is a difficulty in structuring a microscopic-mechanical-vibration filter by a semiconductor process.
The second method not using such a composite material is to increase h·L−2 by changing the beam dimensions in equation 1. However, the increase of h and decrease of L results in a decrease of d/L as an index of deformability, making it difficult to detect a deflection of the beam.
Showing the relationship between a log (L) and a log (h) as to equation 1 and equation 2 in FIG. 23, straight line 191 is a relationship to be determined from equation 1 while straight line 192 is a relationship to be determined from equation 2. In FIG. 23, when selecting L and h in the upper range (area A) than a straight line with an inclination “2” using the current-dimensions point A as a marking point, there is an increase of f while, when selecting L and h in the lower range (area B) of a straight line with an inclination “1”, there is an increase of d/L. Accordingly, the hatched region (area C) is a range of L and h where the resonant frequency can be raised while securing the amount of beam deformation.
It is clear from FIG. 23 that size reduction in both L and h is a necessary condition for increasing the frequency of a mechanical vibration filter. Meanwhile, size reduction of L and h at the same scaling, i.e. decreasing L and h while lying on the straight line having the inclination 1, is a sufficient condition for the hatched region in FIG. 23.
In this manner, in the conventional mechanical resonator, the resonant frequency can be raised by reducing the dimensions of the mechanical vibration body. Nevertheless, the vibration-detecting signal is unavoidably weakened because of decreased beam vibration. Thus, there is a problem of being readily susceptible to disturbance.